Duality for algebras of relevant logics
Duality for algebras of relevant logics
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相关逻辑代数的对偶性
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
A. Urquhart
中科院分区：
文献类型：
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作者：
A. Urquhart
本文定义了一类具有左残差运算的有界分配格序群群，对应于相关逻辑族中的弱系统。通过添加进一步的假设来获得与更强系统相对应的代数。针对这些代数，开发了一种基于普里斯特利对偶理论的分配格对偶理论。然后应用对偶理论来提供对应于更强相关逻辑的对偶空间的表征。
This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.